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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 61 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6800.2.a.a	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}+4q^{11}-3q^{13}+\cdots$
6800.2.a.b	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
6800.2.a.c	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
6800.2.a.d	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
6800.2.a.e	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
6800.2.a.f	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}-2q^{11}+5q^{13}+\cdots$
6800.2.a.g	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+6q^{11}+3q^{13}+q^{17}+\cdots$
6800.2.a.h	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{13}-q^{17}+4q^{19}+\cdots$
6800.2.a.i	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+4q^{11}+q^{13}+\cdots$
6800.2.a.j	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-4q^{11}+q^{13}+\cdots$
6800.2.a.k	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}-2q^{9}-4q^{11}+3q^{13}+\cdots$
6800.2.a.l	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-2q^{11}+6q^{13}-q^{17}+\cdots$
6800.2.a.m	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+2q^{13}-q^{17}+4q^{19}-8q^{23}+\cdots$
6800.2.a.n	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+2q^{13}-q^{17}+4q^{19}+\cdots$
6800.2.a.o	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-5q^{7}-2q^{9}-4q^{11}-3q^{13}+\cdots$
6800.2.a.p	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{13}+q^{17}+4q^{19}+\cdots$
6800.2.a.q	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots$
6800.2.a.r	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+6q^{11}-3q^{13}-q^{17}+\cdots$
6800.2.a.s	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}-5q^{13}+q^{17}+\cdots$
6800.2.a.t	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}+q^{13}+q^{17}+\cdots$
6800.2.a.u	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}-2q^{11}-5q^{13}+\cdots$
6800.2.a.v	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
6800.2.a.w	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-2q^{11}+6q^{13}+q^{17}+\cdots$
6800.2.a.x	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
6800.2.a.y	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}+4q^{11}+3q^{13}+\cdots$
6800.2.a.z	$6800$	$2$	6800.a	1.a	$1$	$1$	$1$	$54.298$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+4q^{11}+3q^{13}+\cdots$
6800.2.a.ba	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-4$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}+(-2-\beta )q^{7}+(3-4\beta )q^{9}+\cdots$
6800.2.a.bb	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-3-\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
6800.2.a.bc	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1+\beta )q^{7}-2\beta q^{9}+\cdots$
6800.2.a.bd	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
6800.2.a.be	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots$
6800.2.a.bf	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}-q^{9}+(2+3\beta )q^{11}+\cdots$
6800.2.a.bg	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
6800.2.a.bh	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
6800.2.a.bi	$6800$	$2$	6800.a	1.a	$1$	$2$	$2$	$54.298$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+\beta )q^{7}+2\beta q^{9}-2q^{11}+\cdots$
6800.2.a.bj	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.564.1	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
6800.2.a.bk	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.568.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(3-2\beta _{1}+\cdots)q^{9}+\cdots$
6800.2.a.bl	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.148.1	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{9}+\cdots$
6800.2.a.bm	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
6800.2.a.bn	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.148.1	None	✓	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
6800.2.a.bo	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.229.1	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{9}+\cdots$
6800.2.a.bp	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.568.1	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(3-2\beta _{1}-\beta _{2})q^{9}+\cdots$
6800.2.a.bq	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.564.1	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
6800.2.a.br	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.1016.1	None	✓	$1$	$0$	$0$	$1$	$0$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
6800.2.a.bs	$6800$	$2$	6800.a	1.a	$1$	$3$	$3$	$54.298$	3.3.940.1	None	✓	$1$	$0$	$0$	$3$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
6800.2.a.bt	$6800$	$2$	6800.a	1.a	$1$	$4$	$4$	$54.298$	4.4.6224.1	None	✓	$1$	$1$	$0$	$-4$	$0$	$-10$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
6800.2.a.bu	$6800$	$2$	6800.a	1.a	$1$	$4$	$4$	$54.298$	4.4.11344.1	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots$
6800.2.a.bv	$6800$	$2$	6800.a	1.a	$1$	$4$	$4$	$54.298$	4.4.11344.1	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{2}+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
6800.2.a.bw	$6800$	$2$	6800.a	1.a	$1$	$4$	$4$	$54.298$	4.4.6224.1	None	✓	$1$	$0$	$0$	$4$	$0$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
6800.2.a.bx	$6800$	$2$	6800.a	1.a	$1$	$5$	$5$	$54.298$	5.5.1981136.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.